Geometric phase of entangled atomic qubits coupled to Lorentzian reservoirs

We consider the unitary time evolution of the joint state of a complex quantum system, composed of two atomic qubits and two sets of Lorentzian reservoirs; two atomic qubits are initially in a maximally entangled state. We study the pure geometric phase for the joint system with the cases of both Markovian and non-Markovian Lorentzian reservoirs as the system undergoes parallel transport, and find that the geometric phase is related to the effective coupling between the entangled qubits and the reservoirs. This distinct result, as compared to that found in the previous studies, is due to the entanglement between the qubits and the reservoirs. Finally, the relation between entanglement and the geometric phase is discussed.